I use several smaller fans (one on a timer, one on a thermostat) to help me get to sleep, and to stay in the temp range I can tolerate. They mix the air quite a bit, but that just seems to confuse the mini split. Still air over many hours is most likely to yield a stable room temp. Add to the mix our central A/C, which I've found I still need to control the humidity (the mini sucks badly at that) and I'm in the same boat as when I started - just with a much quieter system freezing me and soaking me with sweat...
Yes, I have tried closing the house air duct completely. I get 70+% humidity.